Another proof of Grothendieck's theorem on the splitting of vector bundles on the projective line

This note contains another proof of Grothendieck`s theorem on the splitting of vector bundles on the projective line over a field $k$. Actually the proof is formulated entirely in the classical terms of a lattice $\Lambda \cong k[T]^d$,discretelyembeddedintothevectorspace$V \cong K_\infty^d$,where$K_\infty \cong k((1/T))$isthecompletionofthefieldofrationalfunctions$k(T)$attheplace$\infty$ with the usual valuation.